A collection of resources on Transformations of Functions this week. The subject content for GCSE content includes: 13.sketch translations and reflections of a given function and for A Level we have:
From Transum, this wonderful resource, Transformations of Functions shows how various transformations affect the graph of a function. There are 16 possible transformations to try including examples of combinations of transformations. Having chosen your transformation you can try sketching the transformed function before revealing the answer.
Remember that Transum’s index is very helpful, if we look at the Graphs menu, we see numerous activities on graphs, also, on the left hand side activities mapped to a curriculum for graphs.
For some helpful notes, check Mathisfun!. Scroll to the bottom of the page for some multiple choice questions to try. The examples include combinations of transformations.
A very helpful feature of the questions on Mathisfun is the very clear feedback, here for example, we see:
It is very helpful indeed when studying this topic to use graphing software to experiment and try out different functions. Note how easy it is using the Desmos graphing calculator to show a graph and then the same graph after a transformation. For example see here the graph of x2 and (x+a)2 (or click on the image).See these Desmos pages – Transformations and Transformations – Advanced.
This is a lovely resource on GeoGebra, Transformation of Graphs from Steven Fan can be used to explore combinations of transformations.
Looking at MEI’s student tasks, several are available for exploring transformations with instructions for using the software and questions to explore. Tasks are available for Autograph, Casio, Desmos and GeoGebra.
Further helpful resources:
On Dr Frost, GCSE Graph Transformations and for A Level, Graphs and Transformations.for Year 1 and Functions and Graphs for Year 2.
Owen (Owen134866 on TES) has a library of Mathematics Further Mathematics teaching resources, these are really clearly structured with step by step examples. Graphs and Transformations can be found on TES in his A Level Pure Mathematics Year 1/AS Collection and Functions and Graphs which includes combinations of function can be found on TES in his A Level Pure Mathematics Year 2 Collection.
On ck12, 1.7 Function Graphs: Combined Transformations, there are several very useful examples of combining transformations. This content is very clear.
Maths Genie – Transforming Graphs GCSE questions and solutions. Sketching and Transforming Curves A Level questions and solutions.
Corbett Maths Transformations of Graphs practice questions.
On Exam Solutions, we have worked exam questions and helpful video tutorials on Translations of Graphs, reflections and stretches.
Notes from Mathisfun have been mentioned above, further notes include from MathsBitsNotebook.com, this on Transformations of Functions. and the A Level course material from CIMT includes Graph Transforms.